33% of female statistics students have tattoos. Suppose we take a random sample of 15 female statistics students Let X represent the number of students with tattoos...

Let $X$ be a random variable with the following probability distribution: \begin{tabular}{c|ccc} $x$ & -2 & 3 & 5 \\ \hline$f(x)$ & 0.3 & 0.3 & 0.4 \end{tabular} Find the standard deviation of $X$.

The expectation a lacked equals the integral of X times it's probability density function, Which is the integral from 1 to 5 and at times 3/32 X -1 and five -X, which he calls free. The expectation of X squared equals integral of X squared time. It's probability density function, which he calls the indian girl from 1 to 5 X squared Times 3/32, That's -1. And a foreign miners there darks which vehicles 49 or five. The variance is the expectation of X squared miners. The square of the expectation relax. This is 49/5 miners spray squared A Chico's fall over five and the standard deviation is the square root of the variance, which is To Times Square without 5/5.

We have a normal distribution with mean 20 and standard deviation 3.4. We want to find the probability that x is greater than or equal to 30 to do so we're going to turn this problem into one that focuses on Z scores instead of our x values Z scores make it easier to understand probability an area. In terms of the standard normal distribution. Remember the Z score is by definition X minus the mean, divided by the standard deviation. So we can convert are bound of X equals 32. A Z score as follows. Z one equal 30 minus 20 divided by 3.4 is equal to 2.94 Now we can re express this problem in terms of Z score probabilities using probability of Z is greater than equal to 2.94 We can rewrite this as we have on the right as one minus the probability Z is less than or equal to 2.94 And putting the probability in terms of Z less than or equal to, allows us to use what is called a Z. Look up table. Using a Z. Look up table to figure out the exact value of probabilities, the less than or equal to 2.94 We obtain one minus 0.9984 which gives us our final solution have 0.16

We have a normal distribution with mean 20 and standard deviation 3.4. We want to find the probability that x is greater than or equal to 30 to do so we're going to turn this problem into one that focuses on Z scores instead of our x values Z scores make it easier to understand probability an area. In terms of the standard normal distribution. Remember the Z score is by definition X minus the mean, divided by the standard deviation. So we can convert are bound of X equals 32. A Z score as follows. Z one equal 30 minus 20 divided by 3.4 is equal to 2.94 Now we can re express this problem in terms of Z score probabilities using probability of Z is greater than equal to 2.94 We can rewrite this as we have on the right as one minus the probability Z is less than or equal to 2.94 And putting the probability in terms of Z less than or equal to, allows us to use what is called a Z. Look up table. Using a Z. Look up table to figure out the exact value of probabilities, the less than or equal to 2.94 We obtain one minus 0.9984 which gives us our final solution have 0.16

So in this question were given a normally distributed random variable X with mean 15 and standard deviation .25. And we're asked to find the values that are symmetrically located with respect to the mean of X And satisfy this condition if he calls 2.8. So we're basically going to convert this into the Z. And we're going to say that area here is point it. So we're basically looking at These two values and for here um we basically know the rest of the area is .2 so we know two times, the probability. see is less than the left is equals two point two. So the probability easy, yes, Less than the left is equals 2.1. And from our table, the Z left value is minus 1.28 So symmetrically rz right value is 1.28 and converting both of these into our ex left and x right value using the formula is the time standard deviation plus mean, We get the values 14.68 and 15.32